Today, we will start here another important topic of
strength of material i.e. thin cylindrical and spherical shells with the help
of this post.

Thin
cylindrical and spherical shells

Thin cylindrical and spherical shells are also termed
as pressure vessels and such vessels are usually used in various engineering
applications such as for storing the fluid under pressure.

Boilers, LPG cylinders, Air receiver tanks are the
best examples of thin cylindrical shells.

A cylindrical or spherical shell will be considered
as thin cylindrical or spherical shell, if the wall thickness of shell is very
small as compared to the internal diameter of the shell.

Wall thickness of a thin cylindrical and spherical
shell will be equal or less than the 1/20 of the internal diameter of shell.

Let us consider one cylindrical shell as displayed
here in following figure. Fluid is stored here under pressure within the
cylindrical shell. We will first find out here the condition to consider the shell
as thin cylindrical or spherical shell.

d = Internal diameter of the shell

t = Wall thickness of the shell

l = Length of the cylinder

P = Internal pressure of the fluid stored inside the
cylinder

Condition
for thin cylindrical or spherical shell

Wall thickness of thin cylinder < [(1/20) x
Internal diameter]

t < d/20

t/d < 1/20

d/t > 20

This is the condition that we must have to note it
to consider a cylindrical or spherical shell as thin cylindrical or spherical
shell.

As we have recently discussed that pressure vessels
are used to store the fluid under pressure. Therefore, there will be two cases
of failure of cylindrical vessel as mentioned here.

Case: 1

As fluid is stored under pressure inside the cylindrical
shell, pressure will be acting vertically upward and downward over the
cylindrical wall. Pressure vessel will tend to burst as displayed here in
following figure.

Case: 2

As fluid is stored under pressure inside the cylindrical
shell, pressure will be acting at the both ends of the cylindrical wall.
Pressure vessel will tend to burst as displayed here in following figure.